### Abstract

We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This pcrturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

Original language | English |
---|---|

Article number | 064014 |

Journal | Physical Review D |

Volume | 66 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D*,

*66*(6), [064014]. https://doi.org/10.1103/PhysRevD.66.064014

**Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion.** / Tatekawa, Takayuki; Suda, Momoko; Maeda, Keiichi; Morita, Masaaki; Anzai, Hiroki.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 66, no. 6, 064014. https://doi.org/10.1103/PhysRevD.66.064014

}

TY - JOUR

T1 - Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

AU - Tatekawa, Takayuki

AU - Suda, Momoko

AU - Maeda, Keiichi

AU - Morita, Masaaki

AU - Anzai, Hiroki

PY - 2002

Y1 - 2002

N2 - We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This pcrturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

AB - We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This pcrturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

UR - http://www.scopus.com/inward/record.url?scp=4243919079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243919079&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.66.064014

DO - 10.1103/PhysRevD.66.064014

M3 - Article

AN - SCOPUS:4243919079

VL - 66

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 6

M1 - 064014

ER -